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J. Phys. Chem. B 2010, 114, 1174–1179
Controllable Synthetic Molecular Channels: Biomimetic Ammonia Switch Alexey V. Titov, Boyang Wang, Kyaw Sint, and Petr Kra´l* Department of Chemistry, UniVersity of Illinois at Chicago, Chicago, Illinois 60607 ReceiVed: October 30, 2009; ReVised Manuscript ReceiVed: NoVember 25, 2009
We use molecular dynamics simulations combined with iterative screening to test if one can design mechanically controllable and selective molecular pores. The first model pore is formed by two stacked carbon nanocones connected by aliphatic chains at their open tips, in analogy to aquaporins. It turns out that when one nanocone is gradually rotated with respect to the other, the molecular chains alter the size of the nanopore formed at the cone tips and control the flow rates of liquid pentane through it. The second model pore is formed by two carbon nanotubes joined by a cylindrical structure of antiparallel peptides. By application of a torque to one of the nanotubes, while holding the other, we can reversibly fold the peptides into forward or backwardtwisted barrels. We have modified the internal residues in these barrels to make these pores selective and controllable. Eventually, we found a nanopore that in the two folded configurations has very different transmission rates for hydrated NH3 molecules. Introduction Biological ionic and molecular channels play a key role in cellular transport phenomena.1 Most of them are protein channels with cores formed by precisely arranged arrays of amino acids that efficiently recognize and guide the passing species.2 Their selectivity is achieved by intriguing concerted dynamics of the molecular passage through channels with complex Coulombic and van der Waals (vdW) potentials.3 For example, β-barrel channels4 are formed by antiparallel hydrogen-bonded β sheets helically wrapped into cylinders. Other channels can have different symmetries or forms, such as the tetrameric aquaporins5-7 and tetrameric ion channels.8,9 The profile of some biological channels can be modulated in response to voltage gating,10 ligand binding,11 or mechanical deformation.12 Artificial protein channels could be designed de novo13-15 or assembled from legolike pieces16 and fine-tuned by a “directed evolution”.17 Biomimetic constructions of molecular channels can rely on more synthetic approaches.18,19 For example, synthetic channels can be made from ring peptides, coupled by hydrogen bonds,20,21 or Coulombically.22 These systems might be incorporated and activated inside biological membranes.23,24 Ionic and molecular channels could also be made of inorganic materials, such as zeolites,25 carbon,26 silica,27 and other materials.28,29 The inorganic channels are often not selective or transparent enough for various refined applications. Therefore, nanochannels with novel structures and recognition principles need to be designed. Molecular dynamics (MD) simulations have predicted30 and experiments have demonstrated fast transport of gases31,32 and liquids33-35 through carbon nanotube (CNT) membranes. Hydrated ions could pass through CNTs of large enough diameters36 and drag molecules on CNT surfaces.37,38 Nanocones39 with open tips or graphene sheets with nanopores40 could also form nanofluidic channels. Although, the selectivity of these inorganic channels is rather limited,41,42 their passage rates might be controlled mechanically43,44 and electronically.45 These optimistic results show that synthetic functional channels can, in principle, be designed. But there are many open * To whom correspondence should be addressed: E-mail:
[email protected].
Figure 1. The stacked (untwisted) pair of nanocones connected with four -(CH2)13- alkyl chains around the central pore. (left) Bottom view form the tip. (right) The side view.
problems associated with this possibility. Here, we want to explore some of these limitations on model systems that reveal what qualities one might expect in such systems and what obstacles we might need to overcome. In our test studies, we combine the properties of biological and synthetic nanopores to design model hybrid nanochannels, formed by covalently connected carbon nanocones or nanotubes with aliphatic or peptide chains.46 The selectivity of these nanochannels is tuned by mutations of the peptide residues and their transport rates are controlled by their mechanical deformations.47 Results and Discussion Molecular Nanovalve. First, we design a model molecular valve formed by two stacked carbon nanocones with the C4 symmetry,39 as shown in Figure 1. The cone tips have a total disclination angle of TD ) 120° (apex angle 84.6°).48 The inner and outer cones are formed by three and four layers of benzene rings, respectively, and have square open tips with the sizes of 15 × 15 Å2 and 20 × 20 Å2. In principle, one could open the cone tips by oxidation reactions49,50 and realize their bonding
10.1021/jp9103933 2010 American Chemical Society Published on Web 12/11/2009
Controllable Synthetic Molecular Channels with the chains by aromatic substitution reactions.51,52 Four alkyl -(CH2)13- chains are covalently attached to the cones at the corners of their square-shaped tips. In the absence of external forces, these relatively long chains are loosely folded between the two cone tips so that a nanopore is formed at the center. This hybrid system is reminiscent of tetrameric channel proteins, such as aquaporins.5-7 The π-π stacking of the cones allows precise and reproducible rotation of one cone with respect to the other. If we mutually rotate them by a certain angle θrot, the chains become stretched, helically wrapped, and entangled inside the nanopore. Therefore, we should be able to change the nanopore size by changing θrot and control the flow of fluids through it. The MD simulations of the molecular flows through the synthetic nanochannels described here are performed with the NAMD package.53 We estimate parameters of atoms in aliphatic groups, various molecules, CNTs, and nanocones from similar atom types and add them to the CHARMM27 force field.54 The time step is always 2 fs, and the Langevin dynamics is always applied with the damping coefficient 0.01 ps-1 to minimize the unphysical loss of momenta to the reservoirs.37,38 In our MD simulations, we solvate the nanocones with alkyl chains in liquid pentane and study its passage through the nanopore under pressure, when the cones are rotated by the angle θrot. At each rotation configuration, the pressure of P ) 5-140 atm is applied to the pentane molecules, and each simulation runs for t ) 100-500 ns. We count the number of pentanes passing through the pore Np within the simulation time t and calculate the average flow rate R ) Np/t. We simulate the alkane-cone nanovalves in the NVT ensemble. The stacked cones are placed in a periodic box of 47 × 47 × 37 Å3 filled with pentane. The cones are aligned along the z axis and located at -15 Å < z < 0. A layer of fixed dummy atoms is used to cover the plane of the simulation cell around the cones and block the fluid flow around the pore. Initially, the four corners of the outer cone are fixed, and a torque of τ ) 4.8 nN nm is applied to the inner cone to induce their mutual rotation. After the inner cone is rotated by the angles of θrot ) 0, 30, and 60°, the four corners of the inner cone are also fixed. At each θrot, the pressure of P ) 5-140 atm is applied to the pentane molecules, by applying forces to the carbon atoms in all the pentanes in the region of 5 < z < 10 Å. The number of pentanes passing through the nanopore, Np, is calculated by counting the number of molecules passing through a 7 × 7 Å2 square cross section area located at the nanopore center. In this way, we avoid counting largely fluctuating molecular passages through other regions of the system. In Figure 2, we plot the dependence of the flow rates R on the pressure P at θrot ) 0, 30, and 60°. It turns out that R depends dramatically on both parameters. At θrot ) 0°, the cone is practically open and R is nonzero even at small pressures. At large pressures, R grows and is practically proportional to the pressure. At θrot ) 30°, the flow is almost zero at low pressures (P < 10 atm), since the cone is largely closed. At higher pressures, the cross section area of the nanopore becomes bigger,55 and the trend is similar as at θrot ) 0°, but R is almost constant in the region of P ) 10-40 atm. At θrot ) 60°, the flow is practically zero up to P ) 40 atm, where the four alkyl chains start to give up the high pressure. Then, the system gains the usual dependence, although with smaller flows. In the inset of Figure 2, we also show the time dependence of the total number of pentanes that pass the nanopore at P ) 20 atm. The size of the time-dependent fluctuations in Np reflect fluctuations in the sizes of the nanopore, caused by the alkyl chains that rotate and change their conformations. For more
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Figure 2. Dependence of the rate of pentane flow through the nanopore on the applied pressures, at rotation angles of θrot ) 0, 30, and 60°. (inset) The time dependence of total number of pentane molecules that pass the nanopore Np at the applied pressure of P ) 20 atm and different θrot.
closed pores, the fluctuations of Np are smaller, due to stretched alkyl chains. We could further modify these twistable nanopores in order to make them selective to the passing molecules. One possibility is to functionalize the blocking chains. Alternatively, we can avoid connecting the cones by chains and rather attach various functional groups to the cone tips. These functionalized nanocones can be stacked to form longer nanochannels that in their interior might resemble protein channels. Biomimetic Ammonia Switch. In the following, we implement biological components to address the selectiVity issue in our search of controllable synthetic molecular channels. We examine model hybrid nanochannels formed by short peptides stretched between two narrow carbon nanotubes, as shown in Figure 3. The peptide structures could be twisted and folded into a barrel,4 by applying a torque to one of the nanotubes, which thus plays a role of a “chaperon”.56 Once the channels are mutated in their interior, they could potentially have different passage rates in their two (oppositely) folded forms. Because of the large number of possible mutations, we optimally modify the systems57 and screen them for selective molecular flows. The hybrid nanochannels, shown in Figure 3, are formed by 5 pairs of antiparallel peptide strands that are “one-to-one” matched and covalently bonded to the terminal C atoms in two (20,0) CNTs. The C and N termini of the peptide form ester and amide bonds, respectively, with every second carbon (in total 10) at each CNT end. The remaining terminal carbons in the CNTs are replaced by nitrogens, forming embedded quinoline-like structures, which have low vdW coupling to the peptides. The peptide strands used are composed of the Asp, Gly, and aLys amino acids. Here, aLys denotes the (L)-2,3diamino propanoic acid (CR-CH2-NH2 side chain), which has in its side chain three carbons less than lysine. The “parallel” system, shown in a twisted form in the top part of Figure 3, is formed by 5 pairs of antiparallel peptides, each having the structure -aLys-Gly-aLys-Gly- and -Asp-GlyAsp-Gly-. In each pair, one peptide is positively charged, with ∼0.8 e on each aLys residue, while the other (parallel) peptide is negatively charged, with ∼-0.8 e on each Asp residue. The “chessboard” system, shown in the bottom part of Figure 3, is formed by 5 pairs of peptides, each having the structure -aLysGly-Asp-Gly- and -Asp-Gly-aLys-Gly-. The charged residues
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Figure 3. Two types of 12-residue hybrid nanochannels solvated in water at T ) 300 K. (top) The “parallel” structure folds into a helical form under the external torque of τ ≈ 14 nN nm. (bottom) The “chessboard” structure remains straight and ordered for τ < 0.7 nN nm.
in the two systems form a parallel-like and chessboard-like patterns, as shown in the inset of Figure 4. Reversible Folding of Hollow Nanochannels. We investigate first the (hollow) parallel and chessboard nanochannels, formed by peptide strands with 8, 12, and 16 residues and solvated in water. We use MD simulations to investigate their structure, dynamics, and stability, when they are twisted by the applied external torque. During their potential folding under the applied torque, supportive atoms are used to allow rotation and translation of the CNTs around their common axis, and the CNT ends are kept open for the passage of water solvent. We study the folding dynamics and stability of the CNT-peptide-based nanochannel in the NPT ensemble and apply the Langevin Piston method,58 with the pressure of P ) 1 atm and T ) 300 K, in a periodic simulation cell of 38 × 38 × 124 Å3. During the simulations, one CNT is fixed and the other is rotated by a torque τ and left to move freely only in the axial direction, by an external bearing of additional atoms.59 In the absence of torque, both types of structures stay in straight configurations. In the parallel structure, shown in top part of Figure 3, the antiparallel arrangement of the chiral peptides, where positive chains go in one direction and adjacent negative chains go in the other direction, leads to asymmetric Coulombic binding between the neighboring chains and their preferential pairing; this effect is also partly seen in the chessboard structure in the bottom right part of Figure 3. The strong coupling distinguishes this peptide cylinder from the weakly hydrogen-bonded β barrels.4 As a result of the chain pairing, the relatively long structure with 16-residue peptides has the tendency to form randomly distributed openings of the diameter of 4-7 Å, allowing the passage of small molecules. The 8-residue peptides, with much fewer degrees of freedom, form an almost uniform cylinder. In contrast, the chessboard systems have stronger Coulombic attractions both within and between the peptide chains, leading to structures with practically no openings, as shown in the bottom part of Figure 3. In the presence of a small torque, τ < 1.4 nN nm, applied to the two CNTs and oriented in either of the two possible directions, the 8- and 12-residue parallel structures fold within t ≈ 2 ns to twisted but partly disordered forms with “imploded” chains. The water molecules, confined in the interior of the slowly twisting and longitudinally contracting structures, have enough time to diffuse out of their open ends, without providing radial support to the folding chains. When these shorter structures, with fewer degrees of freedom than the 16-residue
Titov et al.
Figure 4. The twist angle-torque hysteresis curve obtained in one cycle for the parallel 8-residue structure. Additional schemes show the charges and their mutual coupling in the straight and twisted structures. (inset) The related Coulombic energy-twist angle hysteresis curve.
structures, are folded under larger torques, water does not have enough time to flow out of them and it applies large pressures on the folding chains, so they are less likely to develop defects. For τ ≈ 14 nN nm, the folding of the 12-residue structure takes only about t ≈ 60 ps, and the folded structure is very ordered and smooth, as shown in the top part of Figure 3. All three (8-, 12-, and 16-residue) parallel structures also fold better under larger Langevin damping, which might be practically realized at lower temperatures or more viscous solvents. This effect is known from protein folding in vitro.60 The misfolded 8 and 12-residue parallel structures can be healed, if we hold them under the torque of τ ) 1.4 nN nm, close their CNT ends, and apply for 1 ns a pressure of P ≈ 200 and 500 atm to the water in their interior, respectively. This large hydrostatic pressure inflates the structures, in analogy to protein folding from disordered to native states. In contrast to the parallel structure, the chessboard systems show resistance to small torques and remain stable in straight forms. At τ > 0.7 nN nm, they fold too but become significantly disordered. We study further only the refoldable (controllable) parallel nanochannels. To understand better their stability, we have exposed them to periodic folding and refolding and analyzed the obtained results. In Figure 4, we present the hysteresis curve for the dependence of the twist angle on the torque applied to the parallel 8-residue structure. The results are obtained in one twisting trajectory going between the two end points (wrapped cylinders) and back, where each data point is averaged over 1000 frames separated by 100 fs, after equilibration for 1 ns. The hysteresis curve is not fully symmetric with respect to the coordinate origin, because the constituent peptides are chiral. The nonzero values of the twist angle at zero torque reflect the Coulombic barriers built in the junction during its folding, similar to natural proteins.60 The stability of these structures is controlled by their free energy G ) H - TS. The entropy S, formed by the vibrational and rotational components, should not change much during the twisting,61 except the backbone rotational entropy that might slightly decrease when the peptide chains get closer to each other. Since ∆Etot ≈ ∆H, we only estimate the total potential energy of the structures. The total energy
Etot ) Etor + Ec + EvdW + Eb + Ea + Ed
(1)
is formed by the torque energy Etor, the Coulombic energy Ec, the van der Waals energy EvdW, the bond stretching energy Eb,
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Figure 5. Axial view of the two twisted configurations of the parallel 4-residue 10-peptide junction, with 2 tryptophan and 2 tyrosine residues in its interior. (left) The tryptophan and tyrosine side chains shadow each other, so the channel is relatively open. (right) The interior side chains are spread, so the channel is blocked more. (bottom) Amino acid sequence map of 4-residue 10-peptide junction. Each column corresponds to a peptide chain, and the odd/even rows are residues with side chains that are exposed outward/inward. Arrows on the sides schematically represent the relative angular displacement for each row upon twisting in the two directions.
the angle bending energy Ea, and the dihedral torsional energy Ed. We approximately evaluate these energies by the VMD package62 for the whole junctions including both CNTs. During the folding, the Eb and Ea energies are almost constant, Ed gets more positive, signaling the rotation of peptide backbones, while EvdW becomes more negative, because the strands gain more contact points. The increase of Ed seems to largely cancel the decrease of EvdW. Therefore, we focus only on the Coulombic energy
Ec )
1 4πε0ε
∑ i
